Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function (original) (raw)
Related papers
Chaos, Solitons & Fractals, 2011
We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings as in Bohm and Kaas [4] while assuming VES production function in the form given by Revankar [24]. It is shown that the model can exhibit unbounded endogenous growth despite the absence of exogenous technical change and the presence of non-reproducible factors if the elasticity of substitution is greater than one. We then consider parameters range related to non-trivial dynamics (i.e. the elasticity of substitution in less than one and shareholders save more than workers) and we focus on local and global bifurcations causing the transition to more and more complex asymptotic dynamics. In particular, as our map is non-differentiable in a subset of the states space, we show that border collision bifurcations occur. Several numerical simulations support the analysis.
Global attractor in Solow growth model with differential savings and endogenic labor force growth
2006
In this paper we study the dynamics of a discrete triangular system T in capital per capita and population growth representing the neoclassical growth model with CES production function and differential savings, under the assumption that the labor force growth rate is endogenous and described by a generic iterative scheme having a unique positive globally stable equilibriumn. The study herewith presented aims at confirming the existence of a compact global attractor for system T along the invariant linen. Consequently asymptotic dynamics of growth models with constant population growth rate can be related to those with non-constant population growth if the steady state rate is globally stable. Furthermore we prove that the system exhibits cycles or even chaotic dynamics patterns if shareholders save more than workers, when the elasticity of substitution between production factors drops below one (so that capital income declines). The analytical results are supplemented by numerical simulations.
Sources of complex dynamics in two-sector growth models
Journal of Economic Dynamics and Control, 1990
This paper develops a tractable multisectoral dynamic equilibrium model and provides a fairly complete analysis of the dynamics that may arise along the intertemporal competitive equilibrium path. Despite the fact that the environment displays neither random nor deterministic variability, the model may produce oscillations in aggregate variables such as output. consumption, and investment.
Nonlinear dynamics in a business-cycle model with logistic population growth
Chaos, Solitons & Fractals, 2009
We consider a discrete-time growth model of the Solow type where workers and shareholders have different but constant saving rates and the population growth dynamics is described by the logistic equation able to exhibit complicated dynamics. We show conditions for the resulting system having a compact global attractor and we describe its structure. We also perform a mainly numerical analysis using the critical lines method able to describe the strange attractor and the absorbing area, in order to show how cyclical or complex fluctuations may be produced in a business-cycle model. We study the dynamic behaviour of the model under different ranges of the main parameters, i.e. the elasticity of substitution between the two production factors and the one in the logistic equation (namely l). We prove the existence of complex dynamics when the elasticity of substitution between production factors drops below one (so that capital income declines) or l increases (so that the amplitude of movements in the population growth rate increases).
Growth and Indeterminacy in Dynamic Models with Externalities
RePEc: Research Papers in Economics, 2010
GROWTH AND INDETERMINACY IN DYNAMIC MODELS WITH EXTERNALITIES' BY MICHELE BOLDRIN AND ALDO RUSTICHINI We study the indeterminacy of equilibria in infinite horizon capital accumulation models with technological externalities. Our investigation encompasses models with bounded and unbounded accumulation paths, and models with one and two sectors of production. Under reasonable assumptions we find that equilibria are locally unique in one-sector economies. In economies with two sectors of production it is instead easy to construct examples where a positive external effect induces a two-dimensional manifold of equilibria converging to the same steady state (in the bounded case) or to the same constant growth rate (in the unbounded case). For the latter we point out that the dynamic behavior of these equilibria is quite complicated and that persistent fluctuations in their growth rates are possible.
The neoclassical growth model with heterogenous quasi-geometric consumers
2003
This paper studies how the assumption of quasi-geometric (quasihyperbolic) discounting affects the individual consumption-savings behavior in the context of the standard one-sector neoclassical growth model with heterogeneous agents. The agents are subject to idiosyncratic shocks and face borrowing constraints. We confine attention to an interior Markov recursive equilibrium. The consequence of quasi-geometric discounting is that the effective discount factor of an agent is not a constant, but an endogenous variable which depends on the agent's current state. We show, both analytically and by simulation, that this feature of the model can significantly affect its distributional implications.
Economic Theory, 2003
We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinitedimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics.
The neoclassical model with variable population change
Proceedings of the 11th WSEAS international …, 2009
We extend the neoclassical growth model with logistic population change introduced by Ferrara and Guerrini [5] by considering a more general law for the population growth rate. In this kind of setup, the model is represented by a two dimensional dynamical system, whose non-trivial steady states, in contrast to the neoclassical model, may be node as well as saddle points.
The Neoclassical Growth Model with Heterogeneous Quasi-Geometric Consumers
Journal of Money, Credit, and Banking, 2006
This paper studies how the assumption of quasi-geometric (quasihyperbolic) discounting affects the individual consumption-savings behavior in the context of the standard one-sector neoclassical growth model with heterogeneous agents. The agents are subject to idiosyncratic shocks and face borrowing constraints. We confine attention to an interior Markov recursive equilibrium. The consequence of quasi-geometric discounting is that the effective discount factor of an agent is not a constant, but an endogenous variable which depends on the agent's current state. We show, both analytically and by simulation, that this feature of the model can significantly affect its distributional implications.